Fortunately—as evidenced since long ago by the existence (as in a medium) of wavelike excitations—the huge connectivity of the neocortex enables coarse-grained or mean-field descriptions, which provide more concise and relevant information to understand the mesoscopic dynamics of the system. Frequently obtained via mean-field techniques and commonly referred to as rate models or neural mass models, coarse-grained reductions have been widely used in the theoretical study of neural systems [1]}, [2]}, [3]}, [4]}. In particular, the one proposed by Wilson and Cowan [1]} has proved to be very useful in describing the macroscopic dynamics of neural circuits. This level of description is able to capture many of the dynamical features associated with several cognitive and behavioral phenomena, such as working memory [2]}, [7]} or perceptual decision making [8]}, [4]}. It is also possible to use a rate model approach to study the dynamics of networks constituted by heterogeneous neurons [10]}, [11]}, thus recovering part of the complexity lost in the averaging. Disposing of an “energy function” (not restricted to symmetric couplings) for rate-level dynamics of neural networks would be a major added advantage.
